A control sample of galaxies is constructed by simultaneously
matching both the redshift and the stellar mass (\(M_*\) ).
The adopted tolerances in the matching are \(|\Delta z|< 0.005\) 
and \(|\Delta \log _{10}M_{*}|< 0.1\) . For each AGN, four control galaxies are
selected. Several types of control samples are constructed.
For the tAGN sample, we construct a control sample, tG\(^{\rm c}\) ,
from the tG sample. For the cAGN sample, a control sample, cG\(^{\rm c}\) ,
is constructed from the cG sample. We also separate galaxies into
a star-forming population and a quiescent population in the SFR-\(M_*\)  space,
using the demarcation line proposed by [1]}.
Thus, for the cAGN sample, we also construct a control
star-forming (cSF\(^{\rm c}\) ) sample and a control quiescent (cQ\(^{\rm c}\) ) sample.
